Question

If $A = \{x : x = 3^n, n \le 6, n \in N\}$ and $B = \{x : x = 9^n, n \le 4, n \in N\}$, then which of the following is incorrect?

• A. $A \cup B = \{3, 9, 27, 81, 243, 729, 6561\}$
• B. $A \cap B = \{9, 81, 729, 6561\}$
• C. $A -B = \{3, 27, 243\}$
• D. $A \Delta B = \{3,27,243,6561\}$

Answer 1

Answer: (B)

$A = \{3^1, 3^2, 3^3, 3^4, 3^5, 3^6\}$
$= \{3, 9, 27, 81, 243, 729\}$
$B = \{9^1, 9^2, 9^3, 9^4\}$
$= \{9, 81, 729, 6561\}$
(a) $A \cup B = \{3, 9, 27, 81, 243, 729, 6561\}$
(b) $A \cap B = \{9, 81, 729\}$
(c) $A - B = \{3, 27, 243\}$
(d) $A \Delta B = (A - B) \cup (B - A)$
$= \{3, 27, 243\} \cup \{6561\}$
$= \{3, 27, 243, 6561\}$